72 Mr. J. Kam on Molecular Attraction and 



II. 



A General Gas Equation which considers the effect of the 

 temperature on the relation of b and /3 to v. 



For the same volume v and total pressure II, the theoretical 

 co-volume l> is by definition inversely proportional to the 

 absolute temperature T. 



If v is the volume of a gas at the pressure II, one time at 

 a temperature 0° C. (T = 273) and another time at T, then 



T 

 v = n.b = —n.bt 



if b and bt are the respective theoretical co-volumes. 



If v is expressed in v =l, 0°, and 11=1 (760 mm.), then 

 the total pressure of the gas is for both temperatures (vide 

 equations (7) & (8)) 



n=^^. 1 =-i-= W + 1 .-V. . . (16a) 



T 



Giving b Q the value <^ • h, 



n= M ±A.- ?r ^ = !i±i. 273 /T . . (i6 ») 



n 1 n n . b t K ' 



in which II is equal either to the pressure of the gas at the 



T 



temperature 0° (T — 273) and the volume -^- . n . b t , or at the 



temperature T and the volume n . b t . In the latter case we 



— jNx molecules of the gas at T from 



273 

 a pressure 11= 7p- to a pressure 11! = II (16 h) if N x was the 



number of molecules of the gas at 0° exerting the pressure II 

 at the volume v. 



If we make the pressure II of a gas at T equal to the 

 pressure II of the same gas at 0° C, and express b f in b , 

 then, if the volumes are expressed in equal multiples n of b 

 and bt, 11 = 1, we have the relation 



n = 



v + b 1_ 1 _ w+1 1 _n + l 273/T 



v ' v v — /3o n ' n . b n ' n . b t 



<f> + b t 273/T 273/T J 





273 P ' 



(16 c) 



